Question

If $a=2i+5j+k$ and $b=4i+mj+nk$ are collinear vectors, then find $m+$ $n$.

Answer 1

Vectors $a$ and $b$ are collinear if

$\frac{2}{4}=\frac{5}{m}=\frac{1}{n}$

$\Rightarrow \frac{5}{m}=\frac{1}{n}=\frac{1}{2}$

$\Rightarrow m=10$ and $n=2$

Therefore $m+n=10+2=12$